v^2-2v+3=-3v+3

Solution for v^2-2v+3=-3v+3 equation:

Simplifying
v2 + -2v + 3 = -3v + 3

Reorder the terms:
3 + -2v + v2 = -3v + 3

Reorder the terms:
3 + -2v + v2 = 3 + -3v

Add '-3' to each side of the equation.
3 + -2v + -3 + v2 = 3 + -3 + -3v

Reorder the terms:
3 + -3 + -2v + v2 = 3 + -3 + -3v

Combine like terms: 3 + -3 = 0
0 + -2v + v2 = 3 + -3 + -3v
-2v + v2 = 3 + -3 + -3v

Combine like terms: 3 + -3 = 0
-2v + v2 = 0 + -3v
-2v + v2 = -3v

Solving
-2v + v2 = -3v

Solving for variable 'v'.

Reorder the terms:
-2v + 3v + v2 = -3v + 3v

Combine like terms: -2v + 3v = 1v
1v + v2 = -3v + 3v

Combine like terms: -3v + 3v = 0
1v + v2 = 0

Factor out the Greatest Common Factor (GCF), 'v'.
v(1 + v) = 0

Subproblem 1
Set the factor 'v' equal to zero and attempt to solve:

Simplifying
v = 0

Solving
v = 0

Move all terms containing v to the left, all other terms to the right.

Simplifying
v = 0
Subproblem 2
Set the factor '(1 + v)' equal to zero and attempt to solve:

Simplifying
1 + v = 0

Solving
1 + v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + v = 0 + -1
v = 0 + -1

Combine like terms: 0 + -1 = -1
v = -1

Simplifying
v = -1
Solution
v = {0, -1}